ARTICLE

Structure of spin excitations in heavily electron-doped Li0.8Fe0.2ODFeSe superconductorsBingying Pan1, Yao Shen 1, Die Hu1, Yu Feng1, J.T. Park 2, A.D. Christianson 3,4, Qisi Wang1, Yiqing Hao1,

Hongliang Wo1, Zhiping Yin5, T.A. Maier6,7 & Jun Zhao 1,8

Heavily electron-doped iron-selenide high-transition-temperature (high-Tc) superconductors,

which have no hole Fermi pockets, but have a notably high Tc, have challenged the

prevailing s± pairing scenario originally proposed for iron pnictides containing both

electron and hole pockets. The microscopic mechanism underlying the enhanced

superconductivity in heavily electron-doped iron-selenide remains unclear. Here, we used

neutron scattering to study the spin excitations of the heavily electron-doped iron-selenide

material Li0.8Fe0.2ODFeSe (Tc= 41 K). Our data revealed nearly ring-shaped magnetic

resonant excitations surrounding (π, π) at ∼21 meV. As the energy increased, the spin

excitations assumed a diamond shape, and they dispersed outward until the energy reached

∼60meV and then inward at higher energies. The observed energy-dependent momentum

structure and twisted dispersion of spin excitations near (π, π) are analogous to those of

hole-doped cuprates in several aspects, thus implying that such spin excitations are essential

for the remarkably high Tc in these materials.

DOI: 10.1038/s41467-017-00162-x OPEN

1 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China. 2 Heinz Maier-Leibnitz Zentrum (MLZ),Technische Universität München, Garching D-85748, Germany. 3Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge,Tennessee 37831-6393, USA. 4 Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA. 5Department of Physicsand Center for Advanced Quantum Studies, Beijing Normal University, Beijing 100875, China. 6 Computer Science and Mathematics Division and Center forNanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA. 7Materials Science and Technology Division, Oak RidgeNational Laboratory, Oak Ridge, Tennessee 37831, USA. 8 Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China. BingyingPan and Yao Shen contributed equally to this work. Correspondence and requests for materials should be addressed to J.Z. (email: zhaoj@fudan.edu.cn)

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Quantitative knowledge of the energy and momentumdependence of the spin excitations of high-temperaturesuperconductors is essential in establishing the

mechanism underlying superconductivity. In iron-pnictidesuperconductors, it is widely believed that the electron pairingis mediated by the stripe spin fluctuations near the nestingwavevector (π, 0) between the hole pockets at the Brillouin zonecenter and the electron pockets at the zone edges (1-Fe unit cell),which typically leads to an s-wave pairing with a sign-reversedgap function (s±)1. However, in the parent phase of iron senlenidesuperconductors FeSe (Tc= 8.7 K), in addition to the stripe spinfluctuations near (π, 0), Néel spin fluctuations near (π, π) wereobserved over a wide energy range2. Moreover, the s± pairingscenario is directly challenged by heavily electron-doped iron-selenides (HEDIS) because these superconductors contain onlyelectron pockets, but not hole pockets3–10. In particular, thewavevector connecting the electron pockets is close to (π, π)rather than (π, 0) in HEDIS, and this raises noteworthy questionsas to how the spin excitation and pairing symmetry evolve as thesystem is tuned into the heavily electron-doped regime in whichsuperconductivity is surprisingly enhanced6, 11–13.

The pairing symmetry in HEDIS is currently under intensetheoretical debate14–25. In experimental studies, scanningtunneling microscopy quasiparticle interference measurementssuggested a sign-preserved s-wave superconducting gap functionbetween electron pockets in single-layer FeSe/SrTiO3 thin films26,whereas low-energy inelastic neutron scattering data revealed amagnetic resonant mode around (π, 0.5π) in AxFe2−ySe2(A=K, Rb…), indicating a sign-reversed superconducting gapfunction27–29. However, the lack of phase-pure single-crystallinesamples have rendered impractical the measurement of themomentum structure of spin excitations over a wider energy rangethroughout the entire Brillouin zone in any HEDIS superconductor.In addition, studies have argued that the coexisting

ffiffiffi5

p×

ffiffiffi5

piron

vacancy ordered antiferromagnetic insulating phase in AxFe2−ySe2and the substrate of the single-layer FeSe/SrTiO3 may influencesuperconductivity30, 31. As yet a complete picture of thespin excitations and the pairing symmetry of a pure bulk single-crystalline HEDIS material remain unclear.

The newly discovered HEDIS Li0.8Fe0.2OHFeSe (Tc = 41 K)exhibits remarkably similar electronic and superconducting gapstructures to those of single layer FeSe/SrTiO3

9, 10, 32, 33.

10 20 30 40

600

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nsity

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s m

in–1

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Q = (0.5, 0.69, 0)

T=2.6 KEf=14.7 meV Ef=34.8 meV

T=45 KT=2.6 KT=45 K

600

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dQ = (0.5, 0.69, 0)E = 21 meV

0 20 40 60

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tens

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cts

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.)

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(0.5, 0.31, 0)

S(5

K)–

S(5

0K)

(mbr

sr–1

meV

–1 f.

u.–1

)

I(2.

6K)–

I(45

K)

(cts

min

–1)

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10 20 30–40

–20

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T=2.6 KT=45 K

Q = (0.5, 0.69, 0)Rocking scan

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nsity

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0K)

(mbr

sr–1

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–1 f.

u.–1

)

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K)–

S(5

0K)

(mbr

sr–1

meV

–1 f.

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17 meV < E < 27 meV

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K (

r.l.u

.)

c f i

Energy (meV) (H, 0.31) (r.l.u.) H (r.l.u.)

40

= (0.5, 0.31, L)Q

Fig. 1 Magnetic resonant mode in Li0.8Fe0.2ODFeSe (Tc= 41 K). a Energy dependence of spin excitations for Li0.8Fe0.2ODFeSe at Q= (0.50, 0.69, 0) in thesuperconducting state (T= 2.6 K) and normal state (45 K). The solid and open circles correspond to the data collected at final energies of Ef= 14.7 and 34.8meV, respectively. b Intensity difference between the superconducting state and normal state (S (2.6 K)–S (45 K)) at (0.50, 0.69, 0) measured onthe PUMA thermal triple-axis spectrometer. The data collected at different Ef were normalized. c Intensity difference between the superconducting stateand normal state (S (5 K)–S (50 K)) at (0.50, 0.31, L) measured on the ARCS time of flight spectrometer (0.5≤ L≤ 4). d Rocking scan near (0.50, 0.69, 0)at E= 21 meV at T= 2.6 K and 45 K. e, f Intensity difference between the superconducting state and normal state (S (5 K)–S (50 K)) along the (H, 0.31)and (0.50, K) directions. g Temperature dependence of the scattering at (0.50, 0.69, 0) and E= 21 meV. h Intensity difference image (S (5 K)–S (50 K)) atE= 22± 5meV. The color bar indicates scattering intensity in unit of mbr sr−1 meV−1 f. u.−1. The white regions in the color plot are gaps between neutrondetectors. i Schematic of the electron Fermi pockets in Li0.8Fe0.2ODFeSe (red) and (Tl,Rb)xFe2−ySe2 (blue) adapted from ref. 9. The calculated resonancewavevector is approximately (0.50, 0.3125) for 0.1 electrons per Fe14, which is consistent with our data (0.50, 0.31). The error bars indicate one standarddeviation

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Particularly, because the phase-pure single-crystalline Li0.8Fe0.2-OHFeSe with a sufficiently large size can be grown,the corresponding intrinsic bulk properties not subject to theinfluence of the interface or impurity phases can be investigated.

In this paper, we report neutron scattering measurements ofthe spin excitations over a wide range of momentum and energyin single-crystalline Li0.8Fe0.2ODFeSe (Tc = 41 K) (“Methods”).Our data revealed nearly ring-shaped magnetic resonant excita-tions at ~21 meV, comprising four elliptical peaks at (π, 0.62π)and equivalent wavevectors surrounding (π, π). The presence ofthe resonance mode surrounding (π, π) indicates a sign reversal inthe superconducting gap function between the electron pockets.As the energy increased, the spin excitations assumed a diamondshape, and they dispersed outward until the energy reached ~60meV and then inward at higher energies, eventually forming a bigblob near (π, π) at 130 meV. Such an energy-dependentmomentum structure and twisted dispersion of spin excitationsnear (π, π) resemble to those in hole-doped cuprates in severalaspects34–37. Our results imply that such spin excitations are anessential ingredient for high temperature superconductivity inthese materials.

ResultsMagnetic resonance mode. We first used the PUMA thermaltriple-axis spectrometer to measure low-energy spin excitationsand their interplay with superconductivity. Figure 1a illustratesthe energy scans at Q= (0.5, 0.69, 0) in the superconducting state(T= 2.6 K) and normal state (T= 45 K), indicating that thescattering at ~21 meV is enhanced below Tc, whereas that atlower energies is suppressed below Tc. To ensure a clear illus-tration of the effect of superconductivity, Fig. 1b presents the plotof the intensity difference associated with the energy scansbetween the superconducting state and normal state, revealing aspin-gap like feature below 18 meV and a resonance mode at ~21meV below the superconducting gap (2Δ≈ 28 meV)9, 38. Asimilar resonance mode at ~20 meV is also revealed near Q=(0.5, 0.31, L) in the data measured on the ARCS time-of-flight(TOF) chopper spectrometer (Fig. 1c). This is consistent with aspin exciton within the superconducting gap when the gap

function exhibited an opposite sign between the electron pocketsat the adjacent zone edges14.

The resonance excitation at 21 meV is further confirmed by theQ-scans near (0.5, 0.69, 0) across Tc. Figure 1d shows that thenormal-state spin excitation (T= 45 K) can be described by asingle Gaussian peak on a linear background and that it issignificantly enhanced on entering the superconducting state(T= 2.6 K). Figure 1g illustrates the detailed temperaturedependence of the scattering, again confirming that theenhancement of the spin excitations is tightly associated withsuperconductivity and behaves like an order parameter below Tc.

To precisely determine the momentum structure of theresonance mode, we used the ARCS spectrometer to map outthe Brillouin zone (“Methods”). The intensity difference imagebetween the superconducting state and normal state [S (5 K)−S(50 K)] near the resonance energy (Fig. 1h) showed elliptical peaksat (0.5, 0.5± δ) and (0.5± δ, 0.5) symmetrically surrounding (0.5,0.5), forming a nearly ring-like structure. The peak position(0.5, 0.5± 0.19) and the anisotropy of the scattering inmomentum space were further confirmed by constant-energycuts, revealing a significant difference between the peak widthsalong the H and K directions (Fig. 1e, f). We noted that theobserved incommensurability δ= 0.19 was smaller than thatobserved (δ≈ 0.25) for the resonance mode in AxFe2−ySe227–29.This is probably because the electron doping level in Li0.8Fe0.2-ODFeSe (~0.08–0.1 electrons per Fe) is lower (less overdoped)than that in AxFe2−ySe2 (~0.18 electrons per Fe)9. Therefore, thelow-energy magnetic scattering in Li0.8Fe0.2ODFeSe is closer to (π,π) compared with that in AxFe2−ySe2 (Fig. 1h, i).

Momentum and energy dependence of high-energy spinexcitations. To acquire a complete picture of the spin excitations,we present in Fig. 2 the evolution of the spin response withenergy. At low energies, the momentum structure of the spinexcitations was similar to that of the resonance mode (Fig. 2a); asthe energy increased, the magnetic response assumed a diamondshape and dispersed outward (Figs. 2b–d). Concurrently, themajor axis of the elliptical peaks was rotated by 90° at energies of~59–66 meV with respect to the axis of those observed at lower

a

0.25

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r.l.u

.)

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r.l.u

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0.75

1

E = 22±1 meV

E = 85±5 meV E = 100±5 meV E = 110±5 meV E = 120±5 meV E = 130±5 meV

E = 39±7 meV E = 66±5 meV E = 74±5 meVE = 59±5 meV

0 0.25 0.5 0.75 1

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1

j

H (r.l.u.)H (r.l.u.)H (r.l.u.)H (r.l.u.)H (r.l.u.)

Fig. 2Momentum dependence of the spin excitations in Li0.8Fe0.2ODFeSe at T= 5 K. a–j Constant-energy images acquired at 5 K and at indicated energies.|Q|-dependent background was subtracted in a–e (Supplementary Note 4). For energies ≥85meV, raw data are presented, f–j. The measurements in a andb–j were conducted at the incident neutron energies of 49.6 and 191.6 meV, respectively. Symmetry equivalent data were collected and averaged toenhance statistical accuracy. The color bar indicates scattering intensity in unit of mbr sr−1 meV−1 f. u.−1

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energy (marked by dashed ellipses in Fig. 2a, d; the rotation of theelliptical peaks is further illustrated in Supplementary Fig. 1).When the energy exceeded 66 meV, the scattering dispersedinward and formed a nearly ring-like pattern at 100 meV, andeventually becoming a big blob near (0.5, 0.5) at 130 meV(Fig. 2e–j). We note that a weak ferromagnetic peak near Q≈ 0,which likely arises from the Li–Fe layer, was revealed by smallangle neutron scattering measurements in polycrystalline(7Li0.82Fe0.18OD)FeSe (Tc= 18 K)39. This wavevector (Q≈ 0) wasnot covered in our measurements in the first Brillouin zone. Wealso did not observe clear ferromagnetic excitations in the secondBrillouin zone, which could be due to the intrinsic weak signaland the decreased magnetic form factor. It is also possible thatour sample which has a different chemical composition and ahigher Tc (41 K) has weaker or no ferromagnetic correlations.

The overall dispersion of the spin excitations in Li0.8Fe0.2-ODFeSe can be seen more clearly in E-Q space. As the energyincreased, the magnetic excitations dispersed outward and theninward (Fig. 3a, b). This dispersion is further confirmed by theconstant-energy cuts along the K direction at various energies inFig. 3c. Such a strongly energy-dependent momentum structureand twisted dispersions of spin excitations are in analogy to thoseof hole-doped cuprate superconductors, which typically

demonstrate the existence of inflection/saddle points in thedispersion curves and the rotation of the scattering pattern acrossinflection/saddle points34–36. On the other hand, spin excitationsin most iron-pnictide superconductors generally disperse outward

2

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2E = 21±2 meV2.03<L<3.36

E = 25±2 meV2.45<L<3.95

E = 28±5 meV1.20<L<1.67

E = 75±5 meV3.27<L<3.84

E = 85±5 meV3.76<L<4.36

E = 95±5 meV4.28<L<4.91

E = 105±5 meV4.83<L<5.50

E = 35±5 meV1.48<L<1.97

E = 45±5 meV1.91<L<2.41

E = 55±5 meV2.34<L<2.86

E = 115±5 meV

E = 125±5 meV

E = 130±5 meV6.36<L<7.17

6.03<L<6.80

5.41<L<6.12

0

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S(Q

, �)

(mbr

sr–1

meV

–1 f.

u.–1

)

S(Q

, �) (m

br sr –1 meV

–1 f.u. –1)

2.80<L<3.34E = 65±5 meV

c

(0.5, K) (r.l.u.) (0.5, K) (r.l.u.)

Fig. 3 Dispersion of the spin excitations in Li0.8Fe0.2ODFeSe at T= 5 K. a Background subtracted E-K slice with incident neutron energy of 191.6 meV. Atwisted dispersion is clearly illustrated. The incident neutron beam was parallel to the c axis and L was coupled with the energy transfer. No L modulationswere observed from the scattering, indicating a two-dimensional nature of the magnetism. The color bar indicates scattering intensity in unit of mbr sr−1

meV−1 f. u.−1. b Dispersion acquired from the constant energy cuts in c. The horizontal error bars represent the full-width at half-maximum of the Gaussianpeaks in c; the vertical error bars represent the energy integration interval. The curves are guides to the eye. c Constant energy cuts along the (0.5, K)direction at the indicated energies and energy/L integration interval. The measurements were conducted at incident neutron energies of 49.6 and 191.6meV. The peak positions are determined by fitting with Gaussian profiles convoluted with the instrumental resolution, with a correction of the Fe2+

magnetic form factor. The error bars indicate one standard deviation. We note that the magnetic intensities in a, c and Fig. 2 are asymmetric because themagnetic form factor drops at larger |Q|

T = 5 KT = 50 K

0 20 40 60 80Energy (meV)

100 120 140

0

10

χ”(�

) (�

B2

eV–1

Fe–1

)

20

30

40

Fig. 4 Energy dependence of the dynamic local susceptibility ofLi0.8Fe0.2ODFeSe at T= 5 and 50 K. The vertical and horizontal barsrepresent the standard deviation and integrated energy interval,respectively. The dashed curves are guides to the eye

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from (π, 0) to (π,± π) which can usually be described by either anitinerant or local moment model1, or the density functionaltheory (DFT) combined with dynamical mean field theory(DMFT) taking into account both correlation effects and realisticband structures40. It should be noted that FeTe-based materialsalso display unusual hourglass-like dispersions41–43. However, themagnetic interaction in FeTe-based materials is very complicatedbecause of the spiral magnetism induced by the interstitial Fe41

and the competition between the double stripe (π/2, π/2) andstripe (π, 0) magnetism40, 44.

Momentum integrated local susceptibility. The use ofphase-pure single crystals enables executing quantitativespin-excitation measurements in absolute units, which has notbeen feasible for phase-separated AxFe2−ySe2. Figure 4 shows

the energy dependence of the local dynamic susceptibilityof Li0.8Fe0.2ODFeSe in absolute units, revealing a two-peakstructure, which is similar to those of iron pnictides and FeSe1, 2,45, 46, although the momentum structures of the spin excitationsin these materials are quite different. The peak of the lowerenergy component corresponds to the resonance mode; thehigher energy component, which carries much more spectralweight, peaked near 60–110 meV (Fig. 4). Notably, the integratedresonance spectral weight (χ5K′′ � χ50K′′ = 0.029(7) μ2B Fe−1) inLi0.8Fe0.2ODFeSe is at least one order of magnitude larger thanthat in bulk FeSe (Tc = 8.7 K). However, the high energy com-ponent of the spectral weight is much lower than that inFeSe2, 47. The effect of the electron-doping seems to entail theconsiderable suppression of high-energy responses andenhancement of low-energy responses. This behavior resembles

0.0 0.2 0.4(0.5, K) (r.l.u.)

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Fig. 5 Calculated dispersion of the spin excitations of Li0.8Fe0.2ODFeSe in the superconducting state. The calculation was done using a BCS/RPA approachdescribed in the main text. a Dispersion of the spin excitations. b–e Momentum structure of the spin excitations at indicated energies. The color barsindicate intensity in arbitrary unit

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that of hole-doped cuprates and hole-doped iron pnictides36, 45,but differs from that of the electron-doped iron pnictides inwhich the high-energy spin excitations were essentially dopingindependent and the superconductivity was completelysuppressed in the over electron-doped regime45. The spinexcitation band widths of Li0.8Fe0.2ODFeSe and FeSe are lowerthan those of most iron pnictides, indicating stronger electroncorrelations in FeSe-based superconductors40.

BCS/RPA calculations and DFT +DMFT calculations. Themagnetism in iron-based materials may arise from either theexchange interaction of the local moments or Fermi surfacenesting of itinerant electrons, or both1. To the best of ourknowledge, the observed energy-dependent momentum structureand twisted dispersion of the spin excitations have not beenpredicted in the known theoretical calculations in HEDIS basedon either a local or itinerant picture. Using a BCS/RPAapproach14, we have calculated the magnetic susceptibility froma 2D tight-binding five-orbital Hubbard–Hund Hamiltonianthat describes the electronic structure of an FeSe system withonly electron pockets14. For the superconducting gap, we haveused a phenomenological dx2�y2 gap ΔðkÞ ¼ Δ0 cos kx � cos ky

� �,

which is close to isotropic on the electron pockets and changessign between them. Previous calculations have shown that thistype of gap structure leads to a neutron resonance in χ(q, ω)near q≈ (π, 0.6π) that arises from scattering between the electronpockets on which the gap changes sign14, 48. The interactionmatrix in orbital space used in the RPA calculation containson-site matrix elements for the intra-orbital and inter-orbitalCoulomb repulsions U and U′, and for the Hunds-rule couplingand pair-hopping terms J and J′, respectively. Here, we have usedspin-rotationally invariant parameters J= J′=U/4 and U′=U/2with U= 0.96 eV. Figure 5a shows the calculated dispersion ofspin excitations as the energy increases and Fig. 5b–e displays itsmomentum structure for different energies. As one sees, themomentum position of the magnetic excitations below 40 meV isbroadly consistent with the experiments (Figs. 3a, b and 5a).However, the BCS/RPA calculations fail to describe the outwarddispersion at higher energies seen in Fig. 3a, b as well as thetwisted momentum structure seen in Fig. 2. We also used acombination of DFT and DMFT, so called DFT +DMFT asimplemented in ref. 40 to compute the electronic structureand spin dynamics of this compound (Supplementary Fig. 2;Supplementary Note 1). Similar to the BCS/RPA calculations,the DFT +DMFT-calculated spin excitation spectra also onlyshow inward dispersion, and no twisted structure is observed(Supplementary Fig. 2i).

DiscussionThe distinct dispersion of spin excitations below and above ~60meV might imply different origins of these excitations. Thelow-energy spin excitations are possibly related to Fermi surfacenesting, as the resonance wavevector and its dopingdependence agree with our BCS/RPA calculations9, 14, 27;whereas, the high-energy spin excitations, which carry morespectral weight, are possibly due to vestigial short-range magneticexchange interactions, as also observed in hole-dopedQ3 cuprates36,37. Regardless of their origins, the spin excitations surrounding(π, π) as well as the electron Fermi pockets connected by (π, π)may interact collaboratively to enhance superconductivity. Thesestructures of spin excitations and Fermi surfaces are analogous tothose of hole-doped cuprates, thus implying that such spinexcitations are a key ingredient for the remarkably high Tc inthese materials.

Recently, we noticed a related paper describing low-energy spinexcitations on Li1−xFexODFe1−ySe powder samples49.

MethodsSample growth and characterizations. Li0.8Fe0.2ODFeSe single crystals weregrown using a hydrothermal method similar to that described in ref. 50, and weredeuterated to reduce the incoherent scattering from hydrogen atoms for theinelastic neutron scattering measurements. Magnetic susceptibility and resistivitymeasurements conducted on a crystal from the same batch as those measured withneutrons showed a sharp superconducting transition at 41 K, signifying the highquality of the crystal. The single crystalline sample was also ground into powder forthe X-ray diffraction refinements (Supplementary Fig. 3; Supplementary Note 2;Supplementary Table 1). The refined structure parameters are consistent with thosein previous reports32.

Inelastic neutron scattering experiments. Inelastic neutron scatteringmeasurements were carried out on the PUMA thermal neutron triple-axisspectrometer (TAS) at the Heinz Maier–Leibnitz Zentrum (MLZ), TU München,Germany, and the ARCS TOF chopper spectrometer at the Spallation NeutronSource of Oak Ridge National Laboratory, USA (Supplementary Note 3). Forthe TAS experiment, ~30 pieces of single crystals with a total mass of 3.2 gwere coaligned in the (H K 0) plane to a mosaicity within ~4°. For the TOFexperiment, 8.5 g crystals were coaligned to a masaicity within ~5°; theincident beam was parallel to the c-axis. The wavevector Q at (qx, qy, qz) is definedas (H, K, L)= (qxa/2π, qya/2π, qzc/2π) reciprocal lattice units (r.l.u.) in the 1-Feunit cell. Here, (0.5, 0.5) and (0.5, 0) correspond to (π, π) and (π, 0), respectively.The |Q|-dependent background was subtracted for the data in Fig. 2a–e followingthe practice of ref. 2 (Supplementary Fig. 4; Supplementary Note 4). Additionallow-energy data are shown in Supplementary Fig. 5 (Supplementary Note 5).The scattering intensity was normalized into absolute units by calibrating it againstthe incoherent scattering of a standard vanadium sample.

Data availability. All data that support the findings of this study are available fromthe corresponding authors upon request.

Received: 14 September 2016 Accepted: 7 June 2017

References1. Dai, P. C. Antiferromagnetic order and spin dynamics in iron-based

superconductors. Rev. Mod. Phys. 87, 855–896 (2015).2. Wang, Q. et al. Magnetic ground state of FeSe. Nat. Commun. 7, 12182 (2016).3. Zhang, Y. et al. Nodeless superconducting gap in AxFe2Se2 (A=K,Cs) revealed

by angle-resolved photoemission spectroscopy. Nat. Mater. 10, 273–277 (2011).4. Qian, T. et al. Absence of a holelike Fermi surface for the iron-based

K0.8Fe1.7Se2 superconductor revealed by angle-resolved photoemissionspectroscopy. Phys. Rev. Lett. 106, 187001 (2011).

5. Mou, D. et al. Distinct Fermi surface topology and nodeless superconductinggap in a (Tl0.58Rb0.42)Fe1.72Se2 superconductor. Phys. Rev. Lett. 106, 107001(2011).

6. Dagotto, E. The unexpected properties of alkali metal iron selenidesuperconductors. Rev. Mod. Phys. 85, 849–867 (2013).

7. He, S. et al. Phase diagram and electronic indication of high-temperaturesuperconductivity at 65 K in single-layer FeSe films. Nat. Mater. 12, 605–610(2013).

8. Tan, S. et al. Interface-induced superconductivity and strain-dependent spindensity waves in FeSe/SrTiO3 thin films. Nat. Mater. 12, 634–640 (2013).

9. Zhao, L. et al. Common electronic origin of superconductivity in (Li,Fe)OHFeSe bulk superconductor and single-layer FeSe/SrTiO3 films. Nat.Commun. 7, 10608 (2016).

10. Niu, X. H. et al. Surface electronic structure and isotropic superconducting gapin (Li0.8Fe0.2)OHFeSe. Phys. Rev. B 92, 060504 (2015).

11. Wang, Q.-Y. et al. Interface-induced high-temperature superconductivity insingle unit-cell FeSe films on SrTiO3. Chin. Phys. Lett. 29, 037402 (2012).

12. Ge, J.-F. et al. Superconductivity above 100 K in single-layer FeSe films ondoped SrTiO3. Nat. Mater. 14, 285–289 (2015).

13. Guo, J. et al. Superconductivity in the iron selenide KxFe2Se2 (0 ≤ x ≤ 1.0).Phys. Rev. B 82, 180520 (2010).

14. Maier, T. A., Graser, S., Hirschfeld, P. J. & Scalapino, D. J. d-wave pairing fromspin fluctuations in the KxFe2−ySe2 superconductors. Phys. Rev. B 83, 100515(2011).

15. Wang, F. et al. The electron pairing of KxFe2−ySe2. Europhys. Lett. 93, 57003(2011).

16. Maiti, S. et al. Evolution of the superconducting state of Fe-based compoundswith doping. Phys. Rev. Lett. 107, 147002 (2011).

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-017-00162-x

6 NATURE COMMUNICATIONS | 8: 123 |DOI: 10.1038/s41467-017-00162-x |www.nature.com/naturecommunications

17. Das, T. & Balatsky, A. V. Stripes, spin resonance, and nodeless d-wave pairingsymmetry in Fe2Se2-based layered superconductors. Phys. Rev. B 84, 014521(2011).

18. Mazin, I. I. Symmetry analysis of possible superconducting states in KxFeySe2superconductors. Phys. Rev. B 84, 024529 (2011).

19. Saito, T., Onari, S. & Kontani, H. Emergence of fully gapped s++-wave andnodal d-wave states mediated by orbital and spin fluctuations in a ten-orbitalmodel of KFe2Se2. Phys. Rev. B 83, 140512 (2011).

20. Pandey, S., Chubukov, A. V. & Khodas, M. Spin resonance in AFe2Se2 withs-wave pairing symmetry. Phys. Rev. B 88, 224505 (2013).

21. Hao, N. N. & Hu, J. P. Odd parity pairing and nodeless antiphase s± iniron-based superconductors. Phys. Rev. B 89, 045144 (2014).

22. Nica, E. M., Yu, R. & Si, Q. Orbital selectivity and emergent superconductingstate from quasi-degenerate s- and d-wave pairing channels in iron-basedsuperconductors. Preprint at http://arxiv.org/abs/1505.04170 (2015).

23. Si, Q., Yu, R. & Abrahams, E. High-temperature superconductivity in ironpnictides and chalcogenides. Nat. Rev. Mater 1, 16017 (2016).

24. Yang, F., Wang, F. & Lee, D. H. Fermiology, orbital order, orbital fluctuations, andCooper pairing in iron-based superconductors. Phys. Rev. B 88, 100504 (2013).

25. Li, Z.-X., Wang, F., Yao, H. & Lee, D.-H. What makes the Tc of monolayer FeSeon SrTiO3 so high: a sign-problem-free quantum Monte Carlo study. Sci. Bull.61, 925–930 (2016).

26. Fan, Q. et al. Plain s-wave superconductivity in single-layer FeSe on SrTiO3

probed by scanning tunnelling microscopy. Nat. Phys 11, 946–952 (2015).27. Park, J. T. et al. Magnetic resonant mode in the low-energy spin-excitation

spectrum of superconducting Rb2Fe4Se5 single crystals. Phys. Rev. Lett. 107,177005 (2011).

28. Taylor, A. E. et al. Spin-wave excitations and superconducting resonant modein CsxFe2−ySe2. Phys. Rev. B 86, 094528 (2012).

29. Friemel, G. et al. Conformity of spin fluctuations in alkali-metal iron selenidesuperconductors inferred from the observation of a magnetic resonant mode inKxFe2−ySez. Europhys. Lett. 99, 67004 (2012).

30. Li, W. et al. KFe2Se2 is the parent compound of K-doped iron selenidesuperconductors. Phys. Rev. Lett. 109, 057003 (2012).

31. Lee, J. J. et al. Interfacial mode coupling as the origin of the enhancement of Tc

in FeSe films on SrTiO3. Nature 515, 245–248 (2014).32. Lu, X. F. et al. Coexistence of superconductivity and antiferromagnetism in

(Li0.8Fe0.2)OHFeSe. Nat. Mater. 14, 325–329 (2015).33. Pachmayr, U. et al. Coexistence of 3d-ferromagnetism and superconductivity in

[(Li1−xFex)OH](Fe1−yLiy)Se. Angew. Chem. Int. Ed. 54, 293–297 (2015).34. Hayden, S. M., Mook, H. A., Dai, P. C., Perring, T. G. & Dogan, F. The

structure of the high-energy spin excitations in a high-transition-temperaturesuperconductor. Nature 429, 531–534 (2004).

35. Tranquada, J. M. et al. Quantum magnetic excitations from stripes in copperoxide superconductors. Nature 429, 534–538 (2004).

36. Vignolle, B. et al. Two energy scales in the spin excitations of thehigh-temperature superconductor La2−xSrxCuO4. Nat. Phys 3, 163–167 (2007).

37. Lipscombe, O. J. et al. Persistence of high-frequency spin fluctuations inoverdoped superconducting La2−xSrxCuO4 (x = 0.22). Phys. Rev. Lett. 99,067002 (2007).

38. Du, Z. et al. Scrutinizing the double superconducting gaps and strong couplingpairing in (Li1−xFex)OHFeSe. Nat. Commun. 7, 10565 (2016).

39. Lynn, J. W. et al. Neutron investigation of the magnetic scattering in aniron-based ferromagnetic superconductor. Phys. Rev. B 92, 060510 (2015).

40. Yin, Z. P., Haule, K. & Kotliar, G. Spin dynamics and orbital-antiphasepairing symmetry in iron-based superconductors. Nat. Phys 10, 845–850 (2014).

41. Stock, C. et al. Soft striped magnetic fluctuations competing withsuperconductivity in Fe1+xTe. Phys. Rev. B 90, 121113 (2014).

42. Zaliznyak, I. A. et al. Unconventional temperature enhanced magnetism inFe1.1Te. Phys. Rev. Lett. 107, 216403 (2011).

43. Li, S. L. et al. Normal-state hourglass dispersion of the spin excitations inFeSexTe1−x. Phys. Rev. Lett. 105, 157002 (2010).

44. Yin, Z. P., Haule, K. & Kotliar, G. Fractional power-law behavior and itsorigin in iron-chalcogenide and ruthenate superconductors: insights fromfirst-principles calculations. Phys. Rev. B 86, 195141 (2012).

45. Wang, M. et al. Doping dependence of spin excitations and its correlations withhigh-temperature superconductivity in iron pnictides. Nat. Commun. 4, 2874(2013).

46. Liu, M. et al. Nature of magnetic excitations in superconductingBaFe1.9Ni0.1As2. Nat. Phys 8, 376–381 (2012).

47. Wang, Q. et al. Strong interplay between stripe spin fluctuations, nematicityand superconductivity in FeSe. Nat. Mater. 15, 159–163 (2016).

48. Friemel, G. et al. Reciprocal-space structure and dispersion of the magneticresonant mode in the superconducting phase of RbxFe2−ySe2 single crystals.Phys. Rev. B 85, 140511 (2012).

49. Davies, N. R. et al. Spin resonance in the superconducting state ofLi1−xFexODFe1−ySe observed by neutron spectroscopy. Phys. Rev. B 94, 144503(2016).

50. Dong, X. L. et al. (Li0.84Fe0.16)OHFe0.98Se superconductor: ion-exchangesynthesis of large single-crystal and highly two-dimensional electron properties.Phys. Rev. B 92, 064515 (2015).

AcknowledgementsThis work was supported by the National Natural Science Foundation of China(Grant No. 11374059), the National Key R&D Program of the MOST of China(Grant No. 2016YFA0300203), and the Ministry of Science and Technology of China(Program 973: 2015CB921302). Z.Y. was supported by the National Natural ScienceFoundation of China (Grant No. 11674030) and the National Key Research andDevelopment Program of China (contract No. 2016YFA0302300). T.A.M. was supportedby the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Sciencesand Engineering Division. A portion of this research used resources at the SpallationNeutron Source, a DOE Office of Science User Facility operated by the Oak RidgeNational Laboratory.

Author contributionsJ.Z. planned the research. D.H., Y.F., and B.P. synthesized the sample. B.P., D.H., Y.S.,Q.W., Y.H., and H.W. characterized the sample. B.P. and Y.S. conducted the neutronexperiments with the experimental assistance from J.T.P. and A.D.C. T.A.M. did theBCS/RPA calculations. Z.Y. performed DFT + DMFT calculations. J.Z., B.P., and Y.S.analyzed the data and wrote the paper.

Additional informationSupplementary Information accompanies this paper at doi:10.1038/s41467-017-00162-x.

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